How can i animate my object with one bone?
The correct procedure in to select in object mode the mesh first, the armature second (with shift select), then press Ctrl P and choose with automatic weights option. In this way moving in pose mode the bone will move the mesh strictly tied. Another (and better) way is to choose the "bone" option, which can be used when the mesh doesn't have to be deformed (in your case, in which you have one bone only, the result is exactly the same).